A consideration on miscibility behaviour in random copolymer blends based on the equation-of-state theory

Abstract

Abstract So-called miscibility and immiscibility windows in random copolymer blends are terms that describe the variation in miscibility with copolymer composition, i.e. immiscible → miscible → immiscible and miscible → immiscible → miscible, respectively. The miscibility has been explained by the change of sign of the intermolecular interaction parameter χ expressed in terms of the intersegmental interaction parameters. For the former and the latter windows the sign of the intermolecular parameter χ changes with copolymer composition from positive → negative → positive and negative → positive → negative, respectively. However, the changing pattern of the sign of χ may depend on temperature because the Flory-Huggins interaction parameter χ depends on temperature. Flory's equation-of-state theory gives two kinds of temperature dependence of χ: (a) a U-shaped curve, which is always positive, and (b) a function increasing monotonically from negative to positive. In this report we discuss, on the basis of Flory's equation-of-state theory, how the pattern of the temperature dependence of χ changes with copolymer composition for copolymer blends. In consequence, even though the sign of χ changes with copolymer composition from positive → negative → positive in a limited temperature range, there were two types of dependences of temperature versus χ curve on copolymer composition: (1) (b) regardless of the copolymer composition as well as (2) (a) → (b) → (a) with copolymer composition predicted by theory. Also, for the blends in which χ changes from negative → positive → negative at a certain temperature, two types were obtained: (3) (b) regardless of the copolymer composition as well as (4) (b) → (a) → (b) with copolymer composition. U-shaped curves can be found only in types (2) and (4); namely in these two types there exists a copolymer composition range where the two polymers are immiscible regardless of temperature. Therefore, it was concluded that so-called miscibility and immiscibility windows should be defined by types (2) and (4), respectively, even though the miscibility change is observed to be immiscible → miscible → immiscible or miscible → immiscible → miscible with copolymer composition in a limited range of temperature.